Exam 6: Introduction to Continuous Probability Distributions

The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds.Given this information,the probability of a sack weighing more than 2.40 pounds is 0.4251.

The standard normal distribution has a mean of 0 and a standard deviation of 1.0.

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work.They can then use the sick leave time any time throughout the year.Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies.The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes.The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes.Assuming that the company wishes no more than 5 percent of all employees to get a cash payment,what should the required number of minutes be?

A study of cars arriving at a parking structure at the local airport shows that the time between arrivals is 1.2 minutes and is exponentially distributed.Based on this information,the mean number of cars arriving per minute is about 0.83.

At the West-Side Drive-Inn,customers arrive at the rate of 10 every 30 minutes.The time between arrivals is exponentially distributed.Given this,what is the mean time between arrivals?

A professor noted that the grades of his students were normally distributed with a mean of 75.07 and a standard deviation of 11.65.If only 10 percent of the students received grades of A,what is the minimum score needed to receive an A?

Watersports Rental at Flathead Lake rents jet skis and power boats for day use.Each piece of equipment has a clock that records the time that it was actually in use while rented.The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours.Watersports management has decided to give a rebate to customers who use the equipment for only a short amount of time.They wish to grant a rebate to no more than 10 percent of all customers.Based on the information provided,the amount of time that should be set as the cut-off between getting the rebate and not getting the rebate is approximately 2.06 hours.

Typically,a continuous random variable is one whose value is determined by measurement instead of counting.

The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S.Army.The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired.However,the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons.The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline.Suppose Varden managers are unwilling to set the mean fill at any level higher than 50 gallons.Given that,in order to meet the requirements,they will need to increase the standard deviation of fill volume.

Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent.What percent of investors at this brokerage hour earned at least 5 percent?

Watersports Rental at Flathead Lake rents jet skis and power boats for day use.Each piece of equipment has a clock that records the time that it was actually in use while rented.The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours.Watersports management has decided to give a rebate to customers who use the equipment for less than 2.0 hours.Based on this information,the probability that a customer will get the rebate is 0.4082.

If the mean,median and mode are all equal for a continuous random variable,then the random variable is normally distributed.

The number of defects manufactured by workers in a small engine plant is an example of a discrete random variable.

The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S.Army.The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired.However,the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons.The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline.In order to meet this requirement,Varden should set the mean fill to approximately 50.225 gallons.

The standard normal distribution table provides probabilities for the area between the z-value and the population mean.

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes.The company is thinking of charging a lower rate for customers who use the phone less than a specified amount.If it wishes to give the rate reduction to no more than 12 percent of its customers,what should the cut-off be?

The amount of drying time for the paint applied to a plastic component part is thought to be uniformly distributed between 30 and 60 minutes.Currently,the automated process selects the part from the drying bin after the part has been there for 50 minutes.The probability that none of three parts picked are still wet when they are selected is approximately 0.04.

Which of the following probability distributions can be used to describe the distribution for a continuous random variable?

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes.What is the probability that three randomly monitored calls will each be completed in 4 minutes or less?

The amount of drying time for the paint applied to a plastic component part is thought to be uniformly distributed between 30 and 60 minutes.Currently,the automated process selects the part from the drying bin after the part has been there for 50 minutes.Based on this,the probability that a part selected will not be dry is approximately 0.33.